Conditional expected utility

Abstract

Abstract. Let E be a class of event. Conditionally Expected Utility decision makers are decision makers whose conditional preferences %E, E 2 E, satisfy the axioms of Subjective Expected Utility theory (SEU). We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We give a representation theorem for a class of such preferences, and show that they are Invariant Bi-separable in the sense of Ghirardato et al. [7]. Then, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn [6].

Generalized Subjective Lexicographic Expected Utility Representation

“…This is consistent with Savage's first formulation of the sure thing principle (page 21, Savage [8]), "Having suggested what I shall tentatively call the sure-thing principle, let me give it relatively formal formal statement thus: If the person would not prefer f to g, either knowing that the event B obtained, or knowing that the event S\B obtained, then he does not prefer f to g. Moreover (provided he does not regard B as virtually impossible) if he would definitely prefer g to f , knowing that B obtained, and, if he would not prefer f to g, knowing that B did not obtain, then he definitely prefers g to f .") Axiom 2 (P 2 1 2 ). For each pair of events A and B such that B ⊆ A, and each pair of acts f and g,…”

“…Axiom 4 (P 4 1 2 ). For each triple of events A, B and C such that B, C ⊆ A, and constant acts f, f ′ , g and g ′ such that f S f ′ and g S g ′ ,…”

“…In particular, in a standard Savage-style framework, we consider a decision maker that is described not only by a preference relation over acts, but also by a family of preference relations over acts. 1 Each preference in this family is indexed by some event in the state space. The idea is that a preference indexed by an event, say A , where A is the indexing event, represents the preferences of the agent when the agent is informed that the event A has occurred.…”

“…This is another question for future research. A related paper is that of Amarante [1], which does allow for infinitely many "informed" (or conditional) preferences by also considering a family of such preferences as a primitive of the model, but does not provide a lexicographic representation, as the focus of the paper is to show that a family of SEU conditional preferences does not necessarily give rise to an SEU unconditional preference.…”

Seismic risk mitigation in buildings using a new method to encode a joint weighting function in multi-attribute utility theory

“…Others argued the proper scoring rules [36][37][38]. Many discussed the expected utility, such as [39][40][41][42][43][44][45], and [46] examined the conditional expected utility. Others discussed ambiguity [47][48][49][50][51][52][53].…”